Parametric Mixture Models: An Advanced Approach to Addressing Complex Hazards in Survival Analysis

OBJECTIVES: Survival modeling is crucial for Health Technology Assessment (HTA) bodies to assess treatments' impacts on survival and health-related quality of life in economic evaluations. Extrapolating beyond follow-up time is critical for evaluating long-term intervention benefits. Current methods use single statistical distributions for extrapolation, but this is challenging with complex hazard functions that do not follow a clear trend during follow-up. The aim of this study is to apply a mixture of two parametric distributions to time-to-event data, considering distinct clusters or sub-populations of patients with varying hazard and survival profiles.

METHODS: Pseudo-IPD, generated using the Guyot algorithm, incorporated two subpopulations with distinct hazard trajectories, resulting in a complex hazard function. Standard parametric models (e.g., Exponential, Weibull, Log-normal, Log-logistic, Gompertz, Gamma, and Generalized Gamma) were fitted to the time-to-event data. Additionally, mixture models combining any two parametric distributions were fitted, allowing for weights to be assigned to different components. Parametric mixture models do not constrain components to have the same distribution; instead, they allow for diverse distributional choices across components. Each mixture component could be adjusted for covariate effects in all parameters, including mixture probabilities, to identify subpopulations that may respond differently to treatment. Model selection criteria (AIC, BIC, visual inspection) were used to determine the optimal distributional combinations and associated weights.

RESULTS: Among the combinations tested, the Weibull and Gamma distributions emerged as the best fit with AIC and BIC scores of 636 and 635, respectively. However, the combination of Log-logistic and Gompertz distributions was identified as the optimal choice among all tested mixtures, achieving an AIC of 538 with weights assigned as 6% and 94%, respectively.

CONCLUSIONS: Parametric mixture models showed lower AIC and BIC values and superior results in visual inspection compared to single parametric models, offering an alternative approach for modeling complex hazards and extrapolating beyond follow-up time-points.